A horga'hn is the symbol of fertility in the culture of the planet Risa. It is used extensively in Risian design, such as being used as door switch panels in Risian dwellings. (ENT episode: "Two Days and Two Nights")
Possession of a carved horga'hn was to call forth its powers, and to display one publicly was meant to indicates that one was seeking jamaharon.
Commander William Riker asked Captain Jean-Luc Picard to acquire a horga'hn for him when the captain visited Risa in 2366, apparently intending that the captain would unwittingly display it to the women at his resort. (TNG episode: "Captain's Holiday")